The present invention relates to fluid measuring instruments and is directed more particularly to a method of calibrating and linearizing the outputs of fluid measuring instruments which utilize transducers that have nonlinear responses.
In measuring the magnitude of a property of a fluid, such as the concentration or partial pressure of a component of interest, it is often necessary to utilize a transducer which has a nonlinear response. In non-dispersive infrared analyzers, for example, the concentration of a gas of interest is measured by means of a gas filled cell, commonly known as a Luft detector, which is illuminated by an infrared source through a sample cell that contains a gas of unknown composition. In such analyzers, the output of the Luft detector is an exponential (Beer's Law) function of the concentration of the gas of interest in the sample cell. Similar nonlinear responses are, however, exhibited by the transducers used in many other types of instruments, such as those which measure the temperature of a gas, the pH of a liquid, etc.
The nonlinearity of the response of many types of transducers creates a number of problems for the instruments in which they are used. One of these problems is that the nonlinearity prevents the property of interest from being determined by simply ratioing the output produced by the transducer during exposure to a sample fluid to the output produced by that transducer during exposure to a calibration fluid. This is because ratioing is a linear process and cannot therefore readily be used with nonlinear functions. Another of these problems is the loss of resolution that results from directly displaying the outputs of nonlinear transducers. Using a nonlinear display, for example, causes the resolution of the instrument to be greater at one end of the display range than at the other. Using a nonlinear display also introduces the inconvenience of having to interpolate between scale divisions of variable spacings.
The above-described problems are often dealt with by making use of linearization circuits. Analog linearization circuits, for example, make use of the nonlinear response of an analog circuit to compensate for the nonlinear response of the transducers with which they are used. Digital linearizing circuits make use of the mathematical processing ability of computerized instruments to solve equations which compensate for the nonlinear response of the detectors with which they are used. Linearizing circuits of the latter type can also operate by referencing look-up tables which are constructed from the equations to be solved.
While the above-mentioned types of linearizing circuits can operate with a moderate degree of accuracy, they can also introduce significant errors into the displayed outputs of the instruments with which they are used. These errors result from the fact that particular transducers often have nonlinear responses which differ from that of the typical transducer for which the linearizing circuit was designed. Such differences can, for example, result from differences in the sensitivity (or gain) of various transducers, or from differences in their zero responses or offsets. Such differences can also arise in a single transducer as its response changes with time, the accumulation of dirt deposits, etc. These differences produce errors by causing linearizing circuits to over- or under-correct for the response of the particular transducers with which they are used.